Access denied means what it says - program's request for accessing specified files was denied, usually due to insufficient privileges.

It's as generic of an issue as it gets and there is a myriad of causes for it. From antivirus interference to using read-only share access, to not having correct owner on the files, to NAS device quirks, etc... literally tens if not hundreds of causes.

It's probably not something you'd like to hear, but it's basically between you and your setup. If it started happening suddenly, you may want to retrace any changes leading up to it, look at the logs. check your configuration...

I don't madly care about the files that it are blocked. Is there a simple filter I can add to the backup to ignore access denied files/errors perhaps? Every single file has a period at the start of its file name which must have something to do with it too (they are all files generated by Mac devices (iphones or OSX). It is just odd that these have never been an issue before and even if permissions changed why only on those types of files.

I have now deleted all the offending files I can but some do not exist at all. I have about 20 files that the backup says it does not have access to but these files simply do not exist (checked for hidden files and even in DOS). Why would the backup error on files that are not there (still gives access denied error for these files that are not in the folders specified).

Names starting with a dot is a bit of a special case in the Unix world. They are called "dotfiles" and if you are backing up to a *nix-based NAS, chances are that what you were seeing is due to some quirk in handling them. Perhaps a quirk introduced just recently, with a new firmware update or something similar.

Why would the backup error on files that are not there

This will be due to "Backup settings" > "Detecting changes" set to "Use snapshot". When enabled, it will cause the program to NOT rescan destination on every run, but rather rely on the file index saved after every run.

You can force a re-scan of destination by starting backup with Go _while holding Ctrl down_. Or you can change "Detecting changes" to "Re-scan".

(still gives access denied error for these files that are not in the folders specified)

Is it reported for the source copy of a file or for its backup copy? The exact path is logged next to the error details.